Answers
In the given trapezoid, the angle ∠ HMA is 120°.
What is trapezoid?A closed polygon or geometry with four sides, four corners, and four angles is called a trapezium. Each pair of a trapezium's opposing sides is parallel to the other.
In the given trapezoid AMHT,
The angle H = 60°.
To find the angle ∠ HMA,
Since, the sum of angle MHT and angle HMA is equal to 180°.
∠ HMA + ∠ MHT = 180°
∠ HMA + 60 = 180
∠ HMA = 120
The required angle ∠ HMA is 120°.
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Related Questions
complete the proof that \triangle fgh△fghtriangle, f, g, h isn't similar to \triangle jih△jihtriangle, j, i, h.\
Answers
By showing that the corresponding sides are not proportional we know that the Triangles △fgh and △jih are not similar.
To prove that triangles △fgh and △jih are not similar, we need to show that at least one pair of corresponding sides is not proportional.
Let's compare the side lengths:
Side fg does not have a corresponding side in △jih.
Side gh in △fgh corresponds to side hi in △jih.
Side fh in △fgh corresponds to side ij in △jih.
By comparing the side lengths, we can see that side gh/hj and side fh/ij are not proportional.
Therefore, triangles △fgh and △jih are not similar.
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Triangle FGH (△FGH) is not similar to triangle JIH (△JIH) because their corresponding angles are not congruent and their corresponding sides are not proportional.
To prove that triangle FGH (△FGH) is not similar to triangle JIH (△JIH), we need to show that their corresponding angles and corresponding sides are not proportional.
1. Corresponding angles: In similar triangles, corresponding angles are congruent. If we compare the angles of △FGH and △JIH, we find that angle F in △FGH corresponds to angle J in △JIH, angle G corresponds to angle I, and angle H corresponds to angle H. Since the corresponding angles in both triangles are not congruent, we can conclude that the triangles are not similar.
2. Corresponding sides: In similar triangles, corresponding sides are proportional. Let's compare the sides of △FGH and △JIH. Side FG corresponds to side JI, side GH corresponds to side IH, and side FH corresponds to side HJ. If we measure the lengths of these sides, we can see that they are not proportional. Therefore, the triangles are not similar.
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A rectangle has a perimeter of 82. If the width of the rectangle is one less than twice the length , find the width of the rectangle .
a. 12
b. 14
c. 23
d. 27
Answers
Answer:
ans:- 14
Step-by-step explanation:
let length = x
so, width= 2x -1
perimeter= 2(l +b)
82 = 2(x+ 2x-1)
41 = 3x - 1
3x = 42
x = 14
Use the example as a model. Simplify the expressions.
t^37=?
i
-i
1
-1
Answers
Answer:
Step-by-step explanation:
\((\iota)^{37}=(\iota)^{36} \times \iota=[(\iota)^2]^{18}\times \iota=(-1)^{18} \iota=\iota\)
Which phrase matches the expression 2(6 + 3n)?
A. Two times a number plus three times a number.
B. The sum of 12 and three times a number.
C. Two times the sum of six and three times a number.
D. Three times a number increased by six.
Answers
Answer:
C. Two times the sum of six and three times a number
Step-by-step explanation:
three times a number=3n
six=6
the sum=+
two times= 2()
it will give us 2(6+3n)
Answer:
B
Step-by-step explanation:
a line passes through (1, 2) and (2, 5). another line passes through (0, 0) and (−4, 3). find the point where the two lines intersect.
Answers
To find the point of intersection between the two lines, we need to determine the coordinates (x, y) where the two lines intersect. Let's start by finding the equations of the two lines.
Line 1:
Given the points (1, 2) and (2, 5), we can find the slope (m1) of the line using the formula:
m1 = (y2 - y1) / (x2 - x1)
m1 = (5 - 2) / (2 - 1) = 3/1 = 3
Using the point-slope form of a line, we can write the equation for Line 1:
y - y1 = m1(x - x1)
y - 2 = 3(x - 1)
y - 2 = 3x - 3
y = 3x - 3 + 2
y = 3x - 1
Equation 1: y = 3x - 1
Line 2:
Given the points (0, 0) and (-4, 3), we can find the slope (m2) of the line using the formula:
m2 = (y2 - y1) / (x2 - x1)
m2 = (3 - 0) / (-4 - 0) = 3/-4 = -3/4
Using the point-slope form of a line, we can write the equation for Line 2:
y - y1 = m2(x - x1)
y - 0 = -3/4(x - 0)
y = -3/4x
Equation 2: y = -3/4x
To find the point of intersection, we set the equations of the two lines equal to each other and solve for x:
3x - 1 = -3/4x
Multiplying both sides by 4 to eliminate the fraction:
12x - 4 = -3x
Bringing the terms with x to one side:
12x + 3x = 4
15x = 4
Dividing both sides by 15:
x = 4/15
Substituting this value of x back into either of the original equations, let's use Equation 1:
y = 3x - 1
y = 3(4/15) - 1
y = 12/15 - 1
y = 4/5 - 1
y = 4/5 - 5/5
y = -1/5
Therefore, the point of intersection of the two lines is (4/15, -1/5).
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The area of a rhombus is 168 square centimeters. If one diagonal is three times as long as the other, what are the lengths of the diagonals to the nearest tenth of a centimeter. With explanation please.
Answers
The lengths of the diagonals are approximately 10.6 cm and 31.8 cm.
To solve this problem, we can use the formula for the area of a rhombus, which is A = (d₁ x d₂)/2, where A is the area, and d₁ and d₂ are the lengths of the diagonals.
We are given that the area of the rhombus is 168 square centimeters, so we can substitute this value into the formula:
=> 168 = (d₁ x d₂)/2.
We are also given that one diagonal is three times as long as the other, so we can express the length of one diagonal in terms of the other: d₁ = 3d₂.
Substituting this expression for d₁ into the formula for the area, we get:
168 = (3d₂xd₂)/2 336 = 3d₂²2 d₂² = 112 d₂ = √(112) = 10.6 (to the nearest tenth of a centimeter)
Using the expression for d₁ in terms of d₂, we can find the length of the other diagonal:
d₁ = 3d₂ = 3(10.6) = 31.8 (to the nearest tenth of a centimeter)
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2v + 18 = 16 - 4(v + 7)
please help, thank you
Answers
Answer:
v=−5
Step-by-step explanation:
2v + 18 = 16 - 4(v + 7)
2v+18=16−4(v+7)
2v+18=16+(−4)(v)+(−4)(7)(Distribute)
2v+18=16+−4v+−28
2v+18=(−4v)+(16+−28)(Combine Like Terms)
2v+18=−4v+−12
2v+18=−4v−12
Add 4v to both sides.
2v+18+4v=−4v−12+4v
6v+18=−12
Subtract 18 from both sides.
6v+18−18=−12−18
6v=−30
Divide both sides by 6.
6v /6 = −30 /6
v=−5
In Exercise (6), we introduced the number of divisors function d. For this function, d: N rightarrow N, where d(n) is the number of natural number divisors of n. A function that is related to this function is the so-called set of divisors function. This can be defined as a function S that associates with each natural number the set of its distinct natural number factors. For example, S(6) = {1, 2, 3, 6} and S(10) = {1, 2, 5, 10}. (a) Discuss the function S by carefully stating its domain, codomain, and its rule for determining outputs. (b) Determine S(n) for at least five different values of n. (c) Determine S(n) for at least three different prime number values of n. (d) Does there exist a natural number n such that card (S(n)) = 1? Explain. [Recall that card (S(n)) is the number of elements in the set S(n).] (e) Does there exist a natural number n such that card (S(n)) = 2? Explain. (f) Write the output for the function d in terms of the output for the function S. That is, write d(n) in terms of S(n). (g) Is the following statement true or false? Justify your conclusion. For all natural numbers m and n, if m notequalto n, then S(m) notequalto S(n). (h) Is the following statement true or false? Justify your conclusion. For all sets T that are subsets of N, there exists a natural number n such that S(n) = T.
Answers
a. The rule for determining outputs is to find the set of all distinct factors b. {1, 2, 4, 5, 10, 20}. c. {1, 5}. d. 1 and itself. e. there exists a natural number n such that card(S(n)) = 2. f. d(n) = card(S(n)). g. False. h. True.
(a) The set of divisors function S is a function from the natural numbers N to sets of natural numbers. Its domain is the set of all natural numbers, and its codomain is the set of all sets of natural numbers. The rule for determining outputs is to find the set of all distinct factors of a given natural number n.
(b) S(6) = {1, 2, 3, 6}, S(10) = {1, 2, 5, 10}, S(12) = {1, 2, 3, 4, 6, 12}, S(15) = {1, 3, 5, 15}, S(20) = {1, 2, 4, 5, 10, 20}.
(c) S(2) = {1, 2}, S(3) = {1, 3}, S(5) = {1, 5}.
(d) No, there does not exist a natural number n such that card(S(n)) = 1. This is because every natural number has at least two distinct natural number factors: 1 and itself.
(e) Yes, there exists a natural number n such that card(S(n)) = 2. This happens when n is a prime number, as its only factors are 1 and itself.
(f) The number of divisors function d(n) is simply the cardinality of the set S(n). That is, d(n) = card(S(n)).
(g) False. For example, S(6) = {1, 2, 3, 6} and S(9) = {1, 3, 9}.
(h) True. Let T be any subset of N. Let n be the product of all the distinct prime factors of all the elements of T. Then S(n) will be precisely the set of elements in T, since the prime factorization of any element in T will be a subset of the prime factors of n.
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3. (a) Show that the following equation has a root between x = 2 and x = 3. In(x)=x-1.5 (b) Use Newton - Raphson method to find an approximate solution for the equation in part (a), with starting value of x = 2. Give your answer correct to 3 decimal places. [Hint: use a maximum of 4 iterations to get the correct result] (c) For the equation given byx+3-2e* = 0: (i) Use the iterative formula x+1 = 2e™" −3 to find an approximate root of the equation with starting value of x = 0, with a maximum of five iterations. Give your answer correct to 2 decimal places. (ii) Use an appropriate graphical method to find all approximate roots of the equation in (i), giving your answers correct to 1 decimal place.
Answers
In part (a), we are asked to show that the equation In(x) = x - 1.5 has a root between x = 2 and x = 3. In part (b), we need to use the Newton-Raphson method to find an approximate solution for the equation with a starting value of x = 2. In part (c)(i), we are asked to use an iterative formula to find an approximate root of the equation x + 3 - 2e^x = 0 with a starting value of x = 0. In part (c)(ii), we need to use a graphical method to find all approximate roots of the equation.
(a) To show that the equation In(x) = x - 1.5 has a root between x = 2 and x = 3, we can evaluate In(x) and x - 1.5 at the endpoints and observe that they have opposite signs. By the Intermediate Value Theorem, there must be at least one root between the two endpoints. (b) To use the Newton-Raphson method, we start with an initial guess of x = 2 and then iteratively update x using the formula x_new = x - f(x)/f'(x), where f(x) = In(x) - x + 1.5. We repeat this process until we reach the desired accuracy or until the maximum number of iterations is reached. (c)(i) Using the given iterative formula x_new = 2e^(-x) - 3, we can apply it iteratively with a starting value of x = 0 for a maximum of five iterations to approximate a root of the equation x + 3 - 2e^x = 0. (c)(ii) To find all approximate roots of the equation x + 3 - 2e^x = 0 using a graphical method, we can plot the function and identify the x-intercepts, which correspond to the roots of the equation. By inspecting the graph, we can estimate the approximate values of the roots.
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A sales associate at an electronics store earns 9.5% commission on her total yearly sales. Last year, the sales associate earned an income of $11,875. What is the total amount of sales that the associate made last
year?
Answers
The total amount of sales made by the associate last year is $124,000.
What is defined as the percentage?The term percent means "out of every hundred" or "per hundred."
The term is based on the Latin phrase per centum, which means "by the hundred." So, for every 100 units of something, a single percent represents one of those hundred units, or one percent.To calculate a percentage, divide the fraction of the total by the total but also multiply by 100.Now, as per the given question;
Let the total sales done by the associate in last year is 'x'.
The commission earned on the total sales is 9.5%
Thus, 9.5% of x can be written as;
= (9.5×x)/100
The total earning from the sales is $11,875.
Thus,
(9.5×x)/100 = 11,875
Simplify the equation to find x.
x = (11,875×100)/9.5
x = 125,000
Therefore, the total sales done by the commissioner in last year was $125,000.
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5 There are 150 men and 250 women in a crowd.
a What fraction of the crowd are men?
Write your answer in its simplest possible form.
b The ratio of married women to unmarried women is 3 to 2.
How many married women are in the crowd?
C More men arrive. The number of men increases by 20%.
How many men are in the crowd now?
d Some of the women leave.
There are now 60 women in the crowd.
What percentage of the women leave?
Answers
Answer:
men=150
women=250
total=400
Step-by-step explanation:
a) fraction of men
men/total=150/400=15/40
men/total =3/8
b)let married be x
so unmarried wil be 250-x
married/unmarried=3/2
x / 250-x =3/2
x =3(250-x)/2
2x =750-3x
5x=750
x=750/5
x =150
married =150
unmarried=250-150=100
c)20% of men will be :20x150
100
: 30
no of men =150+20%
=150+30
=180
d)no. of women decreased=250-60
=190
percentage of women leaved=% x 250
100
190x100/250=%
76 =%
76% women leaved
It took too much time
MARK ME BRAINLIEST THANKS MY ANSWER PLEASE
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For each journey between work and home, Arjun uses 1.3 gallons of petrol. Arjun has 52 litres of petrol in his car. How many complete journeys between work and home can he do?
1 gallon = 4.5 litres.
Answers
Answer: 9 full journeys
Step-by-step explanation:
4.5 litres * 1.3 gallons = 5.8 litres of petrol
52 litres ÷ 5.8 litres of petrol = 8.9 journeys ≈ 9 full journeys
Worth 60 points for a rapid reply- find the area of each regular polygon. Answers are rounded to the nearest whole number.
Answers
The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
How to calculate for the area of the polygonArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of octagon × (n)number of side.
apothem = s/[2tan(180/n)].
11 = s/[2tan(180/12)]
s = 11 × 2tan15
s = 5.8949
perimeter = 5.8949 × 12 = 70.7388
Area of dodecagon = 1/2 × 11 × 70.7388
Area of dodecagon = 389.0634 in²
Area of pentagon = 1/2 × 5.23 × 7.6
Area of pentagon = 19.874 in²
Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
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14. Which linear function has the greatest initial value?
Function A
x 0,2,4,6
y 0,5,10,15
Function B
y=3x-1
Function C
it's a graph
Answers
Answer:
C
Step-by-step explanation:
The y intercept is the highest
Given f (x) = x2 + 5x + 6, what is [picture included] equal to?
h2 + 14h
2x + h + 5
h + 4
9 + h
![Given f (x) = x2 + 5x + 6, what is [picture included] equal to? h2 + 14h 2x + h + 5 h + 4 9 + h](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/SGIFk4uiNO6yoLEmhBpOoJsAMqETru3R.png)
Answers
The difference quotient evaluated in x = 2 gives:
[ f(2 + h) - f(2)]/h = h + 9
So the last option is the correct one.
How to find the difference quotient evaluated in 2?
Here we know the function:
f(x) = x^2 + 5x + 6
And we want to find the difference quotient:
[ f(2 + h) - f(2)]/h
Let's evaluate the function:
f(2 + h) = (2 + h)^2 + 5*(2 + h) + 6
= 2^2 + h^2 + 4h + 10 + 5h + 6
= h^2 + 9h + 20
f(2) = 2^2 + 5*2 + 6
f(2) = 4 + 10 + 6 = 20
Then we have:
[ f(2 + h) - f(2)]/h
[h^2 + 9h + 20 - 20]/h
[h^2 + 9h ]/h
Taking the quotient we get:
[h^2 + 9h ]/h = h + 9
So the correct option is the last one.
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Which of the following is equivalent to ( 16 3/2) 1/2
Answers
Answer:16 ^ 1.5 (or 3/2) = 64
64 ^ 0.5 (or 1/2) = 8
8 should be your answer
Step-by-step explanation:
y= 2x -1
2x + 3y =13
Answers
Step-by-step explanation:
Check the image above dear.....
What is one of the major uses of physical geography?
Answers
Answer:
Its purpose is to understand how the Earth's physical environment is the basis for, and is affected by, human activity
Step-by-step explanation:
Include steps please and thank you.
Answers
Answer:
U=32m
Step-by-step explanation:
Big triangle
Little triangle
Compare lengths & find scale factor (s.f)
We've got base lengths, that's what we will use to find the scale factor.
27.3 ÷ 15.6 = 1.75 s.f
We're going from big triangle, to small; so, divided by 1.75s.f to find length of u
56 ÷ 1.75 = 32
U= 32m
Hope this helps!
y cant people just put the answer y do they have to put all the things like just put a,b,c,d or ect...
Answers
what do you mean bruv?
N O R M A L people put the answer up top
complete the division equation. How many times does jack need to fill the glass?
Answers
Answer:
Alot
Step-by-step explanation:
Think abt it
2. Calculate the length of the altitude h in ABC, given that m
Answers
Answer:
To find h the altitude we use sine
sin ∅ = opposite / hypotenuse
From the question
AC is the hypotenuse
h is the opposite
sin 29 = h / 23
h = 23 sin 29
h = 11.1506
h = 11.00mm to the nearest hundredth
Hope this helps you
what is mm to meters?
Answers
The method to convert milimeter to meters will be through multiplication of \( {10}^{-3} \) with the quantity in milimeter.
The abbreviation mm is representative of milimeters. Now, we know that milimeters is 1/1000 meters and hence is smaller unit in comparison to meters.
Based on the above mentioned fact, we can multiply the same number (smaller unit) with negative exponent. It will be carried out like this -
Quantity in meters = quantity in milimeter ×
\( {10}^{-3} \), where \( {10}^{-3} \) has negative exponent. Let us say we have 10⁹ milimeters and need to convert in into meters.
So, quantity in meter = 10⁹ × \( {10}^{-3} \),
Performing multiplication which will be done through subtraction of powers
Quantity in meters = 10⁶ meters
Hence, mm to meters will be multiplication with \( {10}^{-3} \).
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can you please help me with Michelson Morley , methods or
procedure ,labeled tables that will allow me to draw the graph ,
also draw the graph for me.
answer all questions correctly step by step
Answers
The Michelson-Morley experiment was conducted in 1887 to detect the existence of the luminiferous ether, which was thought to be the medium through which light traveled.
Here is the procedure for the Michelson-Morley experiment:
1. Set up a light source, a half-silvered mirror, two mirrors, and two detectors in a square configuration.
2. Split the light beam using the half-silvered mirror so that one beam goes to one mirror and the other beam goes to the other mirror.
3. Reflect the beams back to the half-silvered mirror and combine them to produce an interference pattern.
4. Rotate the entire apparatus by 90 degrees and repeat the measurement.
5. Compare the interference patterns from the two orientations.
If there is a luminiferous ether, the speed of light should be faster in the direction of the ether flow and slower in the perpendicular direction. This should produce a difference in the interference patterns.
However, the Michelson-Morley experiment showed that there was no difference in the interference patterns, indicating that the luminiferous ether did not exist.
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Multiply and simplify.
(t+8)(3+³+41+5)
Hint:
1. Multiply
t(3t³+4t+5)
2. Multiply 8(3t³ +4t+5)
3. Combine LIKE terms.
Answers
3t^4 + 24t + 4t^2 + 37t + 40
Steps to multiply and simplify:
Multiply t with each term inside the second bracket: t(3) + t(³) + t(4) + t(1) = 3t + ³t + 4t + t = 8t
Multiply 8 with each term inside the second bracket: 8(3) + 8(³) + 8(4) + 8(1) = 24 + ³24 + 32 + 8 = 72 + ³24
Combine like terms: 8t + 72 + ³24
Final simplified expression: 8t + 72 + ³24
The graph of a quadratic function with vertex (-3,1) is shown in the figure below. Find the range and the domain
Answers
The domain of the given quadratic function is { -3 }
and range is { 1 }
What is a domain and range ?A function's domain is the set of values that can be plugged into it. This set symbolizes the x values in a function like f. (x). Additionally, we can deduce that a function's range refers to the set of values it can accept. There are values in this set that the function returns when we enter an x value.
The domain of the given quadratic function is { -3 }
and range is { 1 }
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Ms. Wilson purchased a welcome mat for her front porch that is a semicircle. The straight side of the mat is 38 inches. To the nearest hundredth, what is the area of the porch mat?
Answers
Answer:
567.06 in.²
Step-by-step explanation:
The mat is a semicircle.
The straight side is a diameter.
d = 38 in.
r = d/2 = 19 in.
Area of circle = πr²
Area of semicircle = πr²/2
A = 3.14159 × (19 in.)² / 2
A = 567.06 in.²
On a piece of paper, use a protractor to construct a triangle with angle measures of 20° and 30°.
Which statements about this triangle are true?
A: It is an acute triangle.
B: The third angle measures 130°.
C: The third angle measures 50°.
D: It is an obtuse triangle.
E: Two sides have the same length.
F: All sides have different lengths.
Answers
the only way to have two or more sides with the same length is to have congruent angles, which is not the case here.
What is triangle?A triangle is a geometric shape that has three sides and three angles. It's one of the simplest polygonal shapes in figure and is extensively used in numerous areas of mathematics, wisdom, engineering, and everyday life. Triangles can be classified in colorful ways grounded on the length of their sides, the measure of their angles, and their overall shape. Some common types of triangles include equilateral triangles, isosceles triangles, scalene triangles, acute triangles, right triangles, and blunt triangles. Triangles have numerous important parcels and formulas associated with them, similar as the Pythagorean theorem, which relates the sides of a right triangle, and the Law of Cosines and Law of Sines, which can be used to find the sides and angles of any triangle.
Given by the question.
A: It is an acute triangle. True, because all angles are less than 90°.
B: The third angle measures 130°. False, because the sum of angles in a triangle is always 180°. The sum of the given angles is 20° + 30° + x = 180°, where x is the measure of the third angle. Solving for x gives x = 130°.
C: The third angle measures 50°. True, because x = 50° (see explanation for statement B).
D: It is an obtuse triangle. False, because an obtuse triangle has one angle greater than 90°, and all angles in this triangle are less than 90°.
E: Two sides have the same length. False, because we cannot determine the length of the sides from the given information about the angles.
F: All sides have different lengths. True, because we cannot determine the length of the sides from the given information about the angles.
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alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. how many calories are in one cookie?
Answers
Since, Alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. Therefore, In a cookie there are 110 calories.
A calorie is a unit of energy that food and drink provide. we can usually find out how many calories are listed in foods, and wearables like the best fitness trackers let you monitor how many calories you're burning in different activities. Certain foods, such as processed foods, tend to be high in calories. Other foods, such as fresh fruits and vegetables, tend to be low in calories. there is not. Calories are needed to give you enough energy to move, keep warm, grow, work, think, and play. Our circulation and digestion also need to work well with the energy we get from calories.
Let x = calories in cookies.
y = calories in carrots.
Now, according to the question:
5x + 2y = 590 --------------------------------------- (1)
3x + 4y = 410 -------------------------------------- (2)
Multiplying equation(1) by 3 and equation(2) by 5:
15x + 6y = 1770 ---------------------------(3)
15x + 20y = 2050 ---------------------------(4)
Solving we get:
y = 280/14
or, y = 20 units.
Putting the value of y = 20 in equation (2)
3x + 4y = 410
⇒ 3x + 4 × 20 = 410
⇒ 3x = 410 - 80
⇒ x = 330/3
⇒ x = 110 Units
Therefore, the calories of cookies is 110 units .
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ellen makes cookies and sells them at the local farmers' market. today, she is going to make batches of her famous cardamom cookies. she has a jar with 2 fluid ounces of cardamom, and her recipe calls for 1 4/5 tablespoons, or 3/10 of a fluid ounce, of cardamom in each batch. how many batches can ellen make with all of her cardamom?
Answers
Ellen can make a maximum of 6 batches of Cardamom cookies with her 2 fluid ounces of cardamom.
Ellen has 2 fluid ounces of cardamom in a jar. Her recipe requires 3/10 of a fluid ounce of cardamom for each batch of cardamom cookies.
We can use division to find the number of batches of cardamom cookies that Ellen can make with all of her cardamom:
2 fluid ounces ÷ (3/10 fluid ounce per batch) = (2/1) ÷ (3/10)
= (2/1) x (10/3)
= 20/3
= 6 2/3
Therefore, Ellen can make 6 batches of cardamom cookies with her 2 fluid ounces of cardamom, with 2/3 of a batch remaining.
Since she cannot make a fraction of a batch, Ellen can make a maximum of 6 batches of cardamom cookies with her 2 fluid ounces of cardamom.
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